Question

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

$\overline{\mathrm{SA}}\parallel \overline{\mathrm{KC}}$;role="math" localid="1637731683825" $\overline{\mathrm{SK}}\parallel \overline{\mathrm{AC}}$

Short answer

The theorem that enables us to deduce from the information given, that quadrilateral SACK is a parallelogram is that if both pairs of the opposite sides of the quadrilateral are parallel then the quadrilateral is a parallelogram.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

It is being given that $\overline{SA}\parallel \overline{KC}$and $\overline{SK}\parallel \overline{AC}$.

That implies it has been given that the opposite sides of the quadrilateral SACK are parallel.

Step 3. Write the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

The theorem that enables us to deduce from the information given, that quadrilateral SACK is a parallelogram is that if both pairs of the opposite sides of the quadrilateral are parallel then the quadrilateral is a parallelogram.